In a group of animals, 530 are carnivorous and half of 3590 are herbivorous and 95950 are both carnivorous and herbivorous. Total number of all types of animals are

Options

A. `100070`
B. `10070`
C. `100007`
D. None of these

Answer

To solve the problem step by step, we need to find the total number of animals in the group based on the given information.

### Step 1: Identify the number of carnivorous animals.
We are given that there are 530 carnivorous animals.
- **Carnivorous = 530**

### Step 2: Calculate the number of herbivorous animals.
We know that half of 3590 are herbivorous. To find this, we divide 3590 by 2.
- Calculation:
\[ \text{Herbivorous} = \frac{3590}{2} = 1795 \]
- **Herbivorous = 1795**

### Step 3: Identify the number of animals that are both carnivorous and herbivorous.
We are given that there are 95950 animals that are both carnivorous and herbivorous.
- **Both = 95950**

### Step 4: Use the principle of inclusion-exclusion to find the total number of animals.
To find the total number of animals, we use the formula:
\[ \text{Total} = (\text{Carnivorous}) + (\text{Herbivorous}) - (\text{Both}) \]
Substituting the values we have:
\[ \text{Total} = 530 + 1795 + 95950 \]

### Step 5: Perform the addition.
Now, we add these values together:
- First, add 530 and 1795:
\[ 530 + 1795 = 2325 \]
- Now, add this result to 95950:
\[ 2325 + 95950 = 98275 \]

### Final Answer:
The total number of all types of animals is **98275**.

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